Shrinkage estimation of Kelly portfolios

Although the Kelly portfolio is theoretically optimal in maximizing the long-term log-growth rate, in practice this is not always so. In this paper, we first show that the sample plug-in estimator of the Kelly portfolio weights is actually biased, and we then propose an unbiased estimator as an alternative. We further derive a shrinkage estimator under the objective of minimizing the expected growth loss of the actual growth relative to the true growth. An explicit formula for the shrinkage coefficient is established. Statistical properties for the shrinkage coefficient are studied through extensive Monte Carlo simulations, and conditions for obtaining accurate estimates for the shrinkage coefficient are also discussed. The effectiveness of the proposed unbiased and shrinkage Kelly portfolios in reducing the expected growth loss are validated by various simulation studies. It is found that our proposed shrinkage Kelly portfolio has superior performances in growth loss reduction, followed by the unbiased Kelly portfolio, and the sample plug-in Kelly portfolio. The advantages of our proposed unbiased and shrinkage Kelly portfolios for long-term investments are additionally confirmed by stock investment in the U.S. market.     

Optimal capital growth with convex shortfall penalties

The optimal capital growth strategy or Kelly strategy has many desirable properties such as maximizing the asymptotic long-run growth of capital. However, it has considerable short-run risk since the utility is logarithmic, with essentially zero Arrow–Pratt risk aversion. It is common to control risk with a Value-at-Risk (VaR) constraint defined on the end of horizon wealth. A more effective approach is to impose a VaR constraint at each time on the wealth path. In this paper, we provide a method to obtain the maximum growth while staying above an ex-ante discrete time wealth path with high probability, where shortfalls below the path are penalized with a convex function of the shortfall. The effect of the path VaR condition and shortfall penalties is a lower growth rate than the Kelly strategy, but the downside risk is under control. The asset price dynamics are defined by a model with Markov transitions between several market regimes and geometric Brownian motion for prices within a regime. The stochastic investment model is reformulated as a deterministic programme which allows the calculation of the optimal constrained growth wagers at discrete points in time.     

Far from the madding crowd: collective wisdom in prediction markets

We investigate market selection and bet pricing in a repeated prediction market model. We derive the conditions for long-run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities, nor are they always nearer to the truth than the beliefs of all surviving agents. This implies that, in general, prediction market prices are not maximum likelihood estimators of the true probabilities. However, when more than one agent survives, the average price emerging from a prediction market approximates the true probability with lower information loss than any individual belief.     

Momentum in weekly returns: the role of intermediate‐horizon past performance

Gutierrez and Kelly (2008) recently documented momentum in weekly returns. Using the Australian market as a setting, we find that stocks with high 1‐week returns exhibit a continuation in returns up to 1 year after a brief initial return reversal. However, after controlling for the intermediate‐horizon past performance, the continuation in returns after 1‐week returns disappears. These findings suggest that different past investment horizons contain separate information about price momentum and that intermediate‐term trends dominate short‐term trends in driving future returns. Overall, we show that understanding momentum over different horizons facilitates the design of more profitable trading strategies.     

Jai Alai arbitrage strategies

This paper presents arbitrage and risk arbitrage betting strategies for Team Jai Alai. This game is the setting for the analysis and most results generalize to other sports betting situations and some financial market applications. The arbitrage conditions are utility free while the risk arbitrage wagers are constructed according to the Kelly criterion/capital growth theory that maximizes asymptotically long-run wealth almost surely.     

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and ?itkovi? (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk \(\hat{\lambda}\) and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with \(\hat{\lambda}\) and with the leverage being proportional to the investor’s confidence in her estimate.     

Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.     

Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques

We propose a model for constructing Asian funds of hedge funds. We compare the accuracy of forecasts of hedge fund returns using an ordinary least squares (OLS) regression model, a nonparametric regression model, and a nonlinear nonparametric model. We backtest to assess these forecasts using three different portfolio construction processes: an “optimized” portfolio, an equally-weighted portfolio, and the Kelly criterion-based portfolio. We find that the Kelly criterion is a reasonable method for constructing a fund of hedge funds, producing better results than a basic optimization or an equally-weighted portfolio construction method. Our backtests also indicate that the nonparametric forecasts and the OLS forecasts produce similar performance at the hedge fund index level. At the individual fund level, our analysis indicates that the OLS forecasts produce higher directional accuracy than the nonparametric methods but the nonparametric methods produce more accurate forecasts than OLS. In backtests, the highest information ratio to predict hedge fund returns is obtained from a combination of the OLS regression with the Fung–Hsieh eight-factor variables as predictors using the Kelly criterion portfolio construction method. Similarly, the highest information ratio using forecasts generated from a combination of the nonparametric regression using the Fung–Hsieh eight-factor model variables is achieved using the Kelly criterion portfolio construction method. Simulations using risk-adjusted total returns indicate that the nonparametric regression model generates superior information ratios than the analogous backtest results using the OLS. However, the benefits of diversification plateau with portfolios of more than 20 hedge funds. These results generally hold with portfolio implementation lags up to 12 months.     

Rate of return parity and currency crises in experimental asset markets

This paper explores the impact of exchange rate uncertainty on the predictive power of rate of return parity in a laboratory environment, extending the work of Fisher and Kelly [Fisher, E.O., Kelly, F.S., 2000. Experimental foreign exchange markets. Pacific Economic Review 5, 365–388] and Childs and Mestelman [Childs, J., Mestelman, S., 2006. Rate of return parity in experimental asset markets. Review of International Economics 14, 331–347]. While these works use unchanging exchange rates, this paper allows for a change in the exchange rate between laboratory currencies. The data indicate rate of return parity is weakened by the potential for a currency crisis. The results also indicate that currency crises can be caused by self-fulfilling prophecies and that the level of reserves with which a fixed exchange rate is defended impacts the timing of a crisis but does not significantly change the likelihood of a currency crisis.     

Adapting financial rationality: Is a new paradigm emerging?

We discuss the implications of an alternative to the efficient market hypothesis (EMH) the adaptive market hypothesis (AMH). The AMH advances a theoretical basis for a new financial paradigm which can better model such phenomena as the recent financial crisis. The AMH regards the financial market order as evolving, tentative and defined by creative destruction in which trading strategies are introduced, mutate to survive, or face abandonment. The concept of investor rationality is less helpful than the distinction between investment strategies which are more or less well adapted to the prevailing market environment. We outline how a more systematic and grounded basis for behavioural finance can be developed in line with the latter approach. Based on this we develop testable hypotheses allowing the AMH to be distinguished from the EMH. Finally, we discuss how the AMH can aid our understanding of important issues in finance. A central insight is that in the survival of richest, as opposed to fittest, implied by the AMH there is much room for misallocation of resources as price and value uncouple. In this shifting financial market order the regulatory State features as a further market in which the vote market verifies or disrupts market conditions.     

关于在财务会计中采用公允价值的探讨

近年来,美国财务会计准则委员会(FASB)和国际会计准则理事会(IASB)大力倡导会计计量运用面向现在和未来的、以市场为基础的公允价值。本文着重研究并比较IASB和FASB给出的公允价值定义和相关的基本概念,认为公允价值是面向市场、以假想交易为对象的一种估计价格,可以有三级估计,最佳的估计是(相同)资产或负债主市场或最有利市场的价格,指出了它带来的缺陷。文章认为,公允价值计量乃是财务会计发展的大势所趋;如果公允价值得以全面应用,则财务会计将有可能反映企业的价值(或其近似值)。     

A careful re-examination of seasonality in international stock markets: Comment on sentiment and stock returns

In questioning Kamstra, Kramer, and Levi’s (2003) finding of an economically and statistically significant seasonal affective disorder (SAD) effect, Kelly and Meschke (2010) make errors of commission and omission. They misrepresent their empirical results, claiming that the SAD effect arises due to a “mechanically induced” effect that is non-existent, labeling the SAD effect a “turn-of-year” effect (when in fact their models and ours separately control for turn-of-year effects), and ignoring coefficient-estimate patterns that strongly support the SAD effect. Our analysis of their data shows, even using their low-power statistical tests, there is significant international evidence supporting the SAD effect. Employing modern, panel/time-series statistical methods strengthens the case dramatically. Additionally, Kelly and Meschke represent the finance, psychology, and medical literatures in misleading ways, describing some findings as opposite to those reported by the researchers themselves, and choosing selective quotes that could easily lead readers to a distorted understanding of these findings.     

On the conditional pricing effects of beta,size, and book-to-market equity in the Hong Kong market

Using Hong Kong equity stock data, this study examines empirically the pricing effects of beta, firm size, and book-to-market equity, but conditional on market situations, i.e. whether the market is up or down. Evidence supports the hypothesis that, if the risk variable is priced by the market, then there exists a systematic but conditional relation between the risk variable and average return, and this relation takes on opposite directions during up and down markets. However, the significance of the relations is often affected by the changing values of the risk variables as a result of changes in market conditions. Specifically, it is found that all three risk variables, namely beta, size, and book-to-market equity, exhibit conditional pricing effects. This is the first comprehensive study of its kind on Hong Kong market, which provides out-of-sample evidence relative to earlier tests on US data. The findings give important insights into capital market behaviour, which should prove useful in investment management and corporate financial decisions.     

The impact on the market for audit services of aggressive competition by auditors

Supporters of direct uninvited solicitation activities argue that clients can make more informed choices of auditors when auditors are allowed to solicit prospective clients. In banned markets, auditors are allowed to submit bids to provide audit services only when invited by the client. This study provides theoretical models that examine the efficiency of client–auditor alignments in the banned and allowed market. We identify conditions under which realignment differences between the two markets occur and derive client losses in the banned market as compared to the allowed market. We also identify conditions under which independence may be impaired in the allowed market, consistent with the claims of solicitation opponents. However, we believe that, in view of the potential positive effects related to audit pricing and client–auditor alignment, restrictions on advertising or direct uninvited solicitation are not necessarily indicated. Instead, regulators or market mechanisms should insure that the independence (truth-telling) condition is so readily satisfied as to be virtually irrelevant. This can happen in one of two ways: (a) increased scrutiny, leading to an increased likelihood of discovery, or (b) increased penalties when an audit failure is discovered, leading to increased costs of an audit failure, or both.     

社会公平问题的经济法思考

针对中国当前突出的社会公平问题,传统部门法面临着挑战.经济法的公平价值体现在通过保障国家调节和规范国家经济调节权,克服因市场与(或)政府的失灵所带来的不公平.中国当前的社会公平问题是在市场经济条件下产生的,而中国经济法也是为解决市场经济条件下的市场缺陷和社会公平问题而产生的.因此,中国经济法应该担负起解决当前社会公平问题的主要任务,实现其社会公平价值.其价值可以通过制定、完善和实施相关经济法得以实现.     

Who exacerbates the extreme swings in the Chinese stock market?

We investigate which investors buy or sell relatively more on the days when the absolute value of market returns or the daily range of market index prices exceeds 5% in the Chinese stock market. Unlike Dennis and Strickland [Journal of Finance 57(5): 1923–1949 (2002)] who find that institutional investors are buying (selling) more when there is a large market increase (decline) in U.S. equity markets, we find that institutional investors in China are systematically buying more than the less sophisticated individual investors during extreme market swings, particularly on extreme market-down days. We reveal that institutional investors in China (primarily pension funds), provide a stabilizing influence during market downturn days. Our findings highlight the benefits of having active institutional investors in an extremely volatile emerging market dominated by less sophisticated individual investors.     

New Evidence on Risk Factors, Characteristics and the Cross-Sectional Variation of Japanese Stock Returns

This paper examines whether the cross-sectional variations in stock returns are better described by systematic risk factors or by firm characteristics such as book-to-market ratios and market capitalization. It provides new evidence from the Japanese stock market based on the recent sample period from 2002 to 2007, which is not addressed in the existing literature. Also, the new results are derived from the generalized method of moments applied to daily returns. The evidence suggests that both the firm size and book-to-market ratio are significantly related to average return premiums. There is mixed evidence, which tends to lend stronger support to the characteristic model rather than the Fama-French three-factor model as more reflective of the return dynamics in the Japanese stock market.     

Modelling the emergence of the interbank networks

Interbank contagion has become a buzzword in the aftermath of the financial crisis that led to a series of shocks to the interbank market and to periods of pronounced market disruptions. However, little is known about how interbank networks are formed and about their sensitivity to changes in key bank parameters (for example, induced by common exogenous shocks or by regulatory initiatives). This paper aims to shed light on these issues by modelling endogenously the formation of interbank networks, which in turn allows for checking the sensitivity of interbank network structures and hence, their underlying contagion risk to changes in market-driven parameters as well as to changes in regulatory measures such as large exposures limits. The sequential network formation mechanism presented in the paper is based on a portfolio optimization model, whereby banks allocate their interbank exposures while balancing the return and risk of counterparty default risk and the placements are accepted taking into account funding diversification benefits. The model offers some interesting insights into how key parameters may affect interbank network structures and can be a valuable tool for analysing the impact of various regulatory policy measures relating to banks’ incentives to operate in the interbank market.     

On the deflationary effect of government's indexed bonds

We consider government intervention in the capital market by selling indexed bonds and buying non-indexed bonds of equal value. If the profits or losses of this operation are transmitted to the public which takes this into consideration then the government's intervention may have no effect on the economy. Insofar as the assumptions of the model permit real effects of the foregoing policy the impact on the economy tends to be deflationary. In analyzing this tendency a distinction is made between the case where the government intervenes in an existing market and the case where it creates a new market for indexed bonds.